[R] Test for Random Points on a Sphere

[Nordlund, Dan (DSHS/RDA)]

> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-
> project.org] On Behalf Of R. Michael Weylandt
> Sent: Friday, October 05, 2012 11:17 AM
> To: Lorenzo Isella
> Cc: r-help at r-project.org
> Subject: Re: [R] Test for Random Points on a Sphere
> 
> On Fri, Oct 5, 2012 at 5:39 PM, Lorenzo Isella
> <lorenzo.isella at gmail.com> wrote:
> > Dear All,
> > I implemented an algorithm for (uniform) random rotations.
> > In order to test it, I can apply it to a unit vector (0,0,1) in
> Cartesian
> > coordinates.
> > The result is supposed to be a set of random, uniformly distributed,
> points
> > on a sphere (not the point of the algorithm, but a way to test it).
> > This is what the points look like when I plot them, but other then
> > eyeballing them, can anyone suggest a test to ensure that I am really
> > generating uniform random points on a sphere?
> > Many thanks
> >
> 
> Gut says to divide the surface into n bits of equal area and see if
> the points appear uniformly in those using something chi-squared-ish,
> but I'm not aware of a canonical way to do so.
> 
> Cheers,
> Michael
> 
> > Lorenzo
> >

I would be more inclined to use a method which is known to produce a points uniformly distributed on the surface of a sphere and not worry about testing your results.  You might find the discussion at the following link useful.

http://mathworld.wolfram.com/SpherePointPicking.html


Hope this is helpful,

Dan

Daniel J. Nordlund
Washington State Department of Social and Health Services
Planning, Performance, and Accountability
Research and Data Analysis Division
Olympia, WA 98504-5204